The cleaver-swinging psycho who admitted hacking a beloved psychologist to death in her Upper East Side office was sent indefinitely to a locked loony bin yesterday, infuriating family members who had hoped he’d stand trial for murder.

“It’s extremely frustrating,” said Owen Faughey, of Queens, who watched angrily as his sister’s disheveled, wide-eyed killer, David Tarloff, was officially deemed too crazy and handed over to state Department of Mental Hygiene officials.

The schizophrenic, out-of-work telemarketer from Corona, Queens, has admitted he butchered Dr. Kathryn Faughey, 56, while trying to rob her East 79th Street offices in February, and was on course to seek an insanity defense until four court-appointed shrinks found he could not understand the charges against him or assist in his own defense.

Yesterday, Manhattan prosecutors announced they would not fight the shrinks’ finding, leaving Manhattan Supreme Court Justice Charles Solomon no choice but to order he be transferred to a secure mental-health facility.